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Parameter estimation for symmetric correlation functions for an mcgf_rs object.

Source: R/fit_base.R
fit_base.mcgf_rs.Rd

Parameter estimation for symmetric correlation functions for an mcgf_rs object.

Usage

# S3 method for mcgf_rs
fit_base(
  x,
  lag_ls,
  horizon = 1,
  model_ls,
  method_ls = "wls",
  optim_fn_ls = "nlminb",
  par_fixed_ls = list(NULL),
  par_init_ls,
  lower_ls = list(NULL),
  upper_ls = list(NULL),
  other_optim_fn_ls = list(NULL),
  dists_base_ls = list(NULL),
  scale_time = 1,
  rs = TRUE,
  ...
)

Arguments

x

An mcgf_rs object containing attributes dists, acfs, ccfs, and sds.

lag_ls

List of integer time lags.

horizon

Integer forecast horizon.

model_ls

List of base models, each element must be one of spatial, temporal, sep, fs. Only sep and fs are supported when mle is used in model_ls.

method_ls

List of parameter estimation methods, weighted least square (wls) or maximum likelihood estimation (mle).

optim_fn_ls

List of optimization functions, each element must be one of nlminb, optim, other. When use other, supply other_optim_fn_ls.

par_fixed_ls

List of fixed parameters.

par_init_ls

List of initial values for parameters to be optimized.

lower_ls

Optional; list of lower bounds of parameters.

upper_ls

Optional: list of upper bounds of parameters.

other_optim_fn_ls

Optional, list of other optimization functions. The first two arguments must be initial values for the parameters and a function to be minimized respectively (same as that of optim and nlminb).

dists_base_ls

List of lists of distance matrices. If NULL, dists(x) is used. Each element must be a matrix or an array of distance matrices.

scale_time

Scale of time unit, default is 1. lag is divided by scale_time for parameter estimation.

rs

Logical; if TRUE x is treated as a regime-switching, FALSE if the parameters need to be estimated in a non-regime-switching setting.

...

Additional arguments passed to all optim_fn_ls.

Value

A list containing outputs from optimization functions of optim_fn

for each regime.

Details

This functions is the regime-switching variant of fit_base.mcgf(). Arguments are in lists. The length of arguments that end in _ls must be 1 or the same as the number of regimes in x. If the length of an argument is 1, then it is set the same for all regimes. Refer to fit_base.mcgf() for more details of the arguments.

Note that both wls and mle are heuristic approaches when x contains observations from a subset of the discrete spatial domain, though estimation results are close to that using the full spatial domain for large sample sizes.

See also

Other functions on fitting an mcgf_rs: add_base.mcgf_rs(), add_lagr.mcgf_rs(), fit_lagr.mcgf_rs(), krige.mcgf_rs(), krige_new.mcgf_rs()

Examples

data(sim2)
sim2_mcgf <- mcgf_rs(sim2$data, dists = sim2$dists, label = sim2$label)
#> `time` is not provided, assuming rows are equally spaced temporally.
sim2_mcgf <- add_acfs(sim2_mcgf, lag_max = 5)
sim2_mcgf <- add_ccfs(sim2_mcgf, lag_max = 5)

# Fit a regime-switching pure spatial model
fit_spatial <-
    fit_base(
        sim2_mcgf,
        lag_ls = 5,
        model_ls = "spatial",
        par_init_ls = list(c(c = 0.00005, gamma = 0.5)),
        par_fixed_ls = list(c(nugget = 0))
    )
lapply(fit_spatial[1:2], function(x) x$fit)
#> $`Regime 1`
#> $`Regime 1`$par
#>           c       gamma 
#> 0.001496696 0.500000000 
#> 
#> $`Regime 1`$objective
#> [1] 3.325991
#> 
#> $`Regime 1`$convergence
#> [1] 0
#> 
#> $`Regime 1`$iterations
#> [1] 60
#> 
#> $`Regime 1`$evaluations
#> function gradient 
#>       81      144 
#> 
#> $`Regime 1`$message
#> [1] "both X-convergence and relative convergence (5)"
#> 
#> 
#> $`Regime 2`
#> $`Regime 2`$par
#>           c       gamma 
#> 0.004074408 0.500000000 
#> 
#> $`Regime 2`$objective
#> [1] 1.106692
#> 
#> $`Regime 2`$convergence
#> [1] 0
#> 
#> $`Regime 2`$iterations
#> [1] 49
#> 
#> $`Regime 2`$evaluations
#> function gradient 
#>       64      121 
#> 
#> $`Regime 2`$message
#> [1] "both X-convergence and relative convergence (5)"
#> 
#> 

# Fit a regime-switching pure temporal model
fit_temporal <-
    fit_base(
        sim2_mcgf,
        lag_ls = 5,
        model_ls = "temporal",
        par_init_ls = list(
            list(a = 0.8, alpha = 0.8),
            list(a = 0.1, alpha = 0.1)
        )
    )
lapply(fit_temporal[1:2], function(x) x$fit)
#> $`Regime 1`
#> $`Regime 1`$par
#>         a     alpha 
#> 0.4375028 0.3020300 
#> 
#> $`Regime 1`$objective
#> [1] 0.007620233
#> 
#> $`Regime 1`$convergence
#> [1] 0
#> 
#> $`Regime 1`$iterations
#> [1] 14
#> 
#> $`Regime 1`$evaluations
#> function gradient 
#>       20       35 
#> 
#> $`Regime 1`$message
#> [1] "relative convergence (4)"
#> 
#> 
#> $`Regime 2`
#> $`Regime 2`$par
#>         a     alpha 
#> 0.3309062 0.8745089 
#> 
#> $`Regime 2`$objective
#> [1] 0.005785562
#> 
#> $`Regime 2`$convergence
#> [1] 0
#> 
#> $`Regime 2`$iterations
#> [1] 22
#> 
#> $`Regime 2`$evaluations
#> function gradient 
#>       27       52 
#> 
#> $`Regime 2`$message
#> [1] "both X-convergence and relative convergence (5)"
#> 
#> 

# Fit a regime-switching separable model
fit_sep <- fit_base(
    sim2_mcgf,
    lag_ls = 5,
    model_ls = "sep",
    par_init_ls = list(list(
        c = 0.00005,
        gamma = 0.5,
        a = 0.5,
        alpha = 0.5
    )),
    par_fixed_ls = list(c(nugget = 0))
)
lapply(fit_sep[1:2], function(x) x$fit)
#> $`Regime 1`
#> $`Regime 1`$par
#>           c       gamma           a       alpha 
#> 0.001539941 0.500000000 0.452841528 0.345950120 
#> 
#> $`Regime 1`$objective
#> [1] 7.62732
#> 
#> $`Regime 1`$convergence
#> [1] 0
#> 
#> $`Regime 1`$iterations
#> [1] 62
#> 
#> $`Regime 1`$evaluations
#> function gradient 
#>       90      290 
#> 
#> $`Regime 1`$message
#> [1] "relative convergence (4)"
#> 
#> 
#> $`Regime 2`
#> $`Regime 2`$par
#>           c       gamma           a       alpha 
#> 0.004107168 0.500000000 0.328388489 0.853896077 
#> 
#> $`Regime 2`$objective
#> [1] 3.302677
#> 
#> $`Regime 2`$convergence
#> [1] 0
#> 
#> $`Regime 2`$iterations
#> [1] 60
#> 
#> $`Regime 2`$evaluations
#> function gradient 
#>       81      281 
#> 
#> $`Regime 2`$message
#> [1] "relative convergence (4)"
#> 
#>